Dear B. Grispos,
You have hit on one of the primary challenges in identifying any sort of rigorous definition for life - it is notoriously difficult to come up with a well-defined criteria that distinguishes living from nonliving. It certainly makes the task of identifying life's origins very difficult without a proper definition!
I am not particularly satisfied with the definition of life as "a complex self-sustaining chemical network based on carbon biochemistry capable of undergoing Darwinian evolution" either. I don't think it makes a clear distinction between animate and inanimate matter. I discuss why Darwinian evolution may not be a sufficient (although it could certainly be necessary) condition in the essay, but what about for example that carbon is necessary? Carbon is certainly a very special element, but silicon is not completely ruled out as a possible alternative. And "complex self-sustaining chemical network" could describe just about any geochemical cycle. So I agree this definition is not adequate - it can certainly be used to describe a great number of systems, many of which we would not be willing to call alive and worse it may not include systems which are alive! This is why I think more fundamental distinctions may be necessary.
Best,
Sara